From: Gerry Myerson <gerry@mpce.mq.edu.au>
Subject: Progress on Catalan's conjecture
Date: Tue, 12 Dec 2000 17:22:05 +1000
Newsgroups: sci.math
Summary: [missing]

Catalan's conjecture is that 8 & 9 are the only consecutive powers. 
About 25 years ago, Tijdeman found a bound for such pairs, that is, 
he found a number N such that if n & n + 1 are both powers then n < N. 
In principle, this made it a finite problem, but N is so large that 
it's impractical to search every n < N. 

Now Preda Mihailescu of the Swiss Federal Institute of Technology in 
Zurich has found a condition on n which so narrows the search that 
it may be feasible to carry it out. Details at

    http://www.maa.org/mathland/mathtrek_12_4_00.html

I have no connection with the work - all I know is what I read at 
this website. 

Gerry Myerson (gerry@mpce.mq.edu.au)